Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process

Abstract : The Euler scheme is a well-known method of approximation of solutions of stochastic differential equations (SDEs). A lot of results are now available concerning the precision of this approximation in case of equations driven by a drift and a Brownian motion. More recently, people got interested in the approximation of solutions of SDEs driven by a general Lévy process. One of the problem when we use Lévy processes is that we cannot simulate them in general and so we cannot apply the Euler scheme. We propose here a new method of approximation based on the cutoff of the small jumps of the Lévy process involved. In order to find the speed ofconvergence of our approximation, we will use results about stability of the solutions of SDEs.
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Stochastic Processes and their Applications, Elsevier, 2002, 103 (2), pp.311-349. 〈10.1016/S0304-4149%2802%2900191-6〉
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https://hal.univ-cotedazur.fr/hal-00755433
Contributeur : Sylvain Rubenthaler <>
Soumis le : mercredi 21 novembre 2012 - 11:34:40
Dernière modification le : jeudi 3 mai 2018 - 13:32:58

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Sylvain Rubenthaler. Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process. Stochastic Processes and their Applications, Elsevier, 2002, 103 (2), pp.311-349. 〈10.1016/S0304-4149%2802%2900191-6〉. 〈hal-00755433〉

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